Anything that your sensei/coach is not explicitly teaching you is too advanced at one month into your training. Wait until you are shown the throws properly.

All of those throws have the potential to injure your partner badly if applied badly.

Actually, in my club there isn't a set cirriculum.

O-soto-gari was shown to me on day one and it's what I've done consistently during uchikomis. I've tried seoi but the height difference creates a problem. Koshi guruma apparently is not that great of a go-to as my coach told me. I had a black belt show me it.

I should probably just ask what is a good, basic forward throw. Still. I would assume I could badly injure my partner if I did almost any throw wrong.

O-soto-gari was shown to me on day one and it's what I've done consistently during uchikomis. I've tried seoi but the height difference creates a problem. Koshi guruma apparently is not that great of a go-to as my coach told me. I had a black belt show me it.

I should probably just ask what is a good, basic forward throw. Still. I would assume I could badly injure my partner if I did almost any throw wrong.

Tai otoshi is the one that terrifies me particularly when I see a beginner attempting it. There's a tendency to want to power it through when it's not quite working, and pop goes your partner's knee.

Seoi nage is a fantastic throw to start with... the reason it's not working for you is because you've only been trying it for a month. Concentrate on trying to get lower (but not dropping to your knees). You need to get your belt below your partner's belt to execute the throw correctly. Lower, preferably. Make sure your feet are shoulder width apart and pointing in the right direction. Get full contact between your back and your partner's chest. Keep your left elbow up as you're turning and look to the left when you execute the throw.

There's so much in seoi nage that can be applied to virtually every other forward throw. Don't give up on it!

Tai otoshi is the one that terrifies me particularly when I see a beginner attempting it. There's a tendency to want to power it through when it's not quite working, and pop goes your partner's knee.

Seoi nage is a fantastic throw to start with... the reason it's not working for you is because you've only been trying it for a month. Concentrate on trying to get lower (but not dropping to your knees). You need to get your belt below your partner's belt to execute the throw correctly. Lower, preferably. Make sure your feet are shoulder width apart and pointing in the right direction. Get full contact between your back and your partner's chest. Keep your left elbow up as you're turning and look to the left when you execute the throw.

There's so much in seoi nage that can be applied to virtually every other forward throw. Don't give up on it!

Alright, I shall take your advice and work on seoi nage. Perhaps morote seoi.

I am about 6'3" and O-soto-gari and morote-seoi-nage were the throws that worked best for me early on. I also like harai-goshi, hiza-garuma and uchi-mata, but learn those as they come. I think its more likely that you need to learn your footwork and fit and learn to recognize kuzushi more than learn one particular throw. At least that is how I feel as a slightly more advanced than you beginner.

My judo instructor told me that he once witnessed a beginner attempt an uchi mata, but enter nowhere near deeply enough. An uchi mata with lots of separation between tori and uke lets tori’s leg swing freely and forcefully into uke’s crotch. Now my instructor tells white and yellow belts at least not to attempt uchi mata in randori, because taking someone to the emergency room to have his testicles untwisted and surgically pulled back out of the body cavity and back down where they belong is, I suppose, something you don’t necessarily want to do more than once.

My judo instructor told me that he once witnessed a beginner attempt an uchi mata, but enter nowhere near deeply enough. An uchi mata with lots of separation between tori and uke lets tori’s leg swing freely and forcefully into uke’s crotch. Now my instructor tells white and yellow belts at least not to attempt uchi mata in randori, because taking someone to the emergency room to have his testicles untwisted and surgically pulled back out of the body cavity and back down where they belong is, I suppose, something you don’t necessarily want to do more than once.

I'm 6'1" and can't stand seoi nage, personally. My go-to throw is generally harai goshi with an underhook, although I will also do it with an arm wrapped around the head. Uchi mata is all the rage in competitive judo, particularly for tall people, but it's pretty difficult to get right. Your instructor is going to be the one that will be able to figure out what works best for you, in the end, but I would say you could at least ask about harai goshi--it can be used in combination with the osoto gari you are currently working, and if you screw it up you have long enough legs to try ashi guruma.

Foot sweeps are good for those with long legs, and you're not likely to do worse than leave some bruises on your uke's leg if (when) you mess up. I would definitely work on seoinage. It's harder when you're the tall one, but certainly do-able, and you will learn early to bend your knees and get low. Plus everything you learn about pivoting and kuzushi and rotating will apply to other forward throws.

I would definitely stay away from uchi mata for now. It's not an easy throw and it IS very easy to hurt your uke if you screw up. Learn harai-goshi first--the single biggest difference between uchi mata and harai goshi is where your hips are in relation to your uke. You'll also be less likely to leave someone writhing on the mats.